Understanding the dramatically diverse behavior of electrons in different crystal environments demands the precise knowledge of their nature on the atomic length scale. The ability of scanning tunneling microscopy (STM) to map coherent quasiparticle interference (QPI) and emerging Landau levels (LL) has opened up a new avenue to visualize quantum mechanical phenomena and provided a new toolset to study various exotic materials. In this dissertation, I describe STM studies focusing on three distinct classes of materials: heavy fermions, topological materials and bismuth.
In systems hosting an array of magnetic moments, the interaction between the itinerant and localized electrons leads to the formation of heavy fermions. STM measurements performed on the (100) surface of CeCoIn$_5$ demonstrates the quasi-two-dimensional, confined nature of the emerging excitations. The response of the superconducting order parameter to potential defects and magnetic field reveals a nodeless behavior of the $d_{x^2-y^2}$ order parameter in z direction, an elongated vortex structure and a spatially modulated pseudogap phase. By utilizing the tunability of the band structure of CeCoIn$_5$, a combined resonant x-ray scattering (RXS) and STM measurements indicate that the QPI can be detected by RXS.
Strong spin-orbit coupling in certain materials can lead to an inverted bulk band structure and consequently to topologically non-trivial phases. Exploring the QPI on topological (crystalline) insulators demonstrates the scattering of symmetry protected surface states, which can be understood based on the shape and spin texture of these surface states. Combined QPI and LL spectroscopy are used to explore the bulk topological band structure of Dirac semimetals, whereas on a Weyl semimetal the rich variety of scattering wavevectors demonstrates the momentum-dependent delocalization of the surface states into the bulk.
The surface of Bi(111) harbors a two-dimensional electron gas consisting of spin-split surface states of multiple electron and hole pockets. Spectroscopic mapping of the arising quantum Hall state shows that a combination of local strain and many-body Coulomb interactions lift the LL degeneracy to form valley-polarized quantum Hall states. The anisotropic LL wavefunctions with orientation corresponding to broken-symmetry state are imaged on the surface providing a direct spatial signature of a nematic electronic phase.